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IMA Journal of Numerical Analysis Advance Access first published online on April 1, 2009
This version published online on May 19, 2009
IMA Journal of Numerical Analysis, doi:10.1093/imanum/drn078
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Dimension splitting for quasilinear parabolic equations

Eskil Hansen{dagger} and Alexander Ostermann{ddagger}

Institut für Mathematik, Universität Innsbruck, Technikerstraße 13, A-6020 Innsbruck, Austria

{dagger} Corresponding author. Email: eskil.hansen{at}uibk.ac.at

{ddagger} Email: alexander.ostermannt{at}uibk.ac.at

Received on 11 January 2008. Revised on 6 November 2008.


  Abstract

In the current paper we derive a rigorous convergence analysis for a broad range of splitting schemes applied to abstract nonlinear evolution equations, including the Lie and Peaceman–Rachford splittings. The analysis is, in particular, applicable to (possibly degenerate) quasilinear parabolic problems and their dimension splittings. The abstract framework is based on the theory of maximal dissipative operators, and we give both a summary of the used theory and some extensions of the classical results. The derived convergence results are illustrated by numerical experiments.

Key Words: quasilinear parabolic problems; dimension splitting; convergence; degeneracy


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